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Baker's Math: A tutorial

April 27, 2012 - 10:07pm

dmsnyder

Baker's Math: A tutorial

In October, 2008 I posted a formula for Greenstein's Jewish Sour Rye which converted his recipe, which was written in volume measurements, to ingredient weights. I have made this bread many times since, but I've never bothered to calculate the baker's percentages for the formula. I decided to do so today and thought I would post the procedures as a tutorial on “baker's math” for new baker's and others who have just never gotten comfortable with this very valuable tool.

Here is the formula I wrote in 2008.

Ingredients

Wt (g)

First Clear flour

500

Water (80-199ºF)

240

Sea salt

12

Ripe rye sour (100% hydration)

750

Instant yeast

7

Altus (optional)

1/2 cup

Caraway seeds

1 T

Cornmeal for dusting parchment

Cornstarch glaze

Converting the formula to baker's math

Baker's math is a method of expressing the quantity of all ingredients, always expressed as weights, as a proportion of the total flour in the formula. This provides a way of comparing formulas and of easily converting them to make a larger or smaller batch of dough. By convention, the total flour is always 100%. If your formula uses more than one type of flour, their total is 100%. So, to use a simple baguette-type dough as an example, the formula might be:

Ingredients

Baker's %

AP flour

100

Water

65

Salt

2

Instant yeast

1

Total

168

Note that the total is over 100%. This is confusing to many initially. Get used to it. This total baker's percentage is an important number, as you will soon see. Again, this formula does not tell you how much of any ingredient to use, so far, only their proportionate amounts. In fact, knowing these proportions gives you all the information you need to make any amount of dough you need for a bake, whether its 500 g or 100 kg.

We have the ingredient amounts for a “batch” of Greenstein's rye bread, and we want to calculate the baker's percentages, so we can make a bigger (or smaller) batch of dough than the original recipe produces.

This bread uses a rye sour – a rye sourdough starter. When working with a pre-ferment like a poolish or a rye sour, there are two ways of representing it in baker's math. One is to treat it a distinct ingredient, like water or salt. The other is to break the pre-ferment down into its flour and water content and add the flour to the total flour and the water to the total water in the formula. These two approaches are equally accurate, but the second approach provides the more accurate representation of the dough characteristics, especially in regard to hydration. In the following table, I have used the second approach.

The rye sour is 100% hydration. That means that the amount of water in it is exactly equal to the amount of water (water = 100% of total flour.) So, 750 g of rye sour consists of 375 g of rye flour and 375 g of water. Therefore, for example, the total water in the dough consists of the 375 g from the rye sour plus the 240 g added to the final dough.

Total Ingredients

Wt (g)

Calculations

Baker's %

First Clear flour

500

Total flour =500+375=875. 500/875=57.

57

Rye flour

375

Total flour =500+375=875. 375/875=43.

43

Water (80-100ºF)

615

Water/Total flour=615/875=70

70

Sea salt

12

Salt/Total flour=12/875=1.4

1.4

Instant yeast

7

Yeast/Total flour=7/875=0.8

0.8

Total

1509

172.2

Now we can see that the original recipe makes 1509 g of dough. (Well, it is actually more because the weight of the caraway seeds and altus, if used, is not included in these calculations.) Adding up the Baker's percentages, you have 172.2. Think of this as meaning that the dough consists of 172.2 “parts,” 100 of which is flour, 70 of which is water, etc. Recall that these numbers represent the relative amounts of each ingredient.

Scaling the recipe

Now, let us assume you want to make Greenstein's Jewish Sour Rye, but you want to make 600 g loaves, and you want to make two of them. So you will need 1200 g of dough.

Since you know your formula consists of 172.2 parts, to determine the weight of each ingredient needed to make 1200 g of dough, what you need for your calculations is the weight of each part. If the total is 1200 g, you get this by dividing 1200 g by 172.2 parts. This equals 6.97, rounded off. This number is called “the conversion factor.” Now we can calculate the amounts of each ingredient in 1200 g of dough. Weights are rounded to the nearest gram.

Total Ingredients

Baker's %

Calculations

Wt (g)

First Clear flour

57

57x6.97=397

397

Rye flour

43

43x6.97=300

300

Water (80-100ºF)

70

70.6.97=488

488

Sea salt

1.4

1.4x6.97=10

10

Instant yeast

0.8

0.8x6.97=6

6

Total

172.2

1201

What this way of representing the formula does not show is how much rye sour you have to build. However, we know from the original recipe that the weight of the rye sour is 1.5 times the weight of the First Clear flour (See the first table, above.) So, for the 1200 g of dough, we will need 1.5x397=595 g of Rye Sour. In the bread books written for professionals, for example, Hamelman's Bread and Suas' Advanced Bread and Pastry, the formulas have separate tables for “Total Dough” which takes the second approach described above and another for “Final Dough” which takes the first approach. You get the best of both worlds. The “Final Dough” would be as follows:

Final dough ingredients

Wt (g)

Baker's %

First Clear flour

397

100

Water (80-199ºF)

191

48

Sea salt

10

2.4

Ripe rye sour (100% hydration)

596

150

Instant yeast

6

1.4

Total

1200

Altus (optional)

1/2 cup

Caraway seeds

1 T

Cornmeal for dusting parchment

Cornstarch glaze

You can see that, while this representation of the formula is more helpful for making the final dough, the Baker's Percentages distort the ingredient proportions. They make the dough look like it has a lower hydration than it really does, and it makes the amounts of salt and yeast seem very high.

Baker's math is an invaluable tool. Once you understand the basic approach and scale a few of your favorite recipes, it becomes easy to use. After a while, if you use it regularly, it becomes intuitive. You will find yourself doing it in your head as you look at new recipes. You can use it for modifying recipes you want to tweak. It will make you a better baker. It is not yet known if it prevents senile dementia, but I bet it helps. I'll let you know, if I remember to.

Addendum 5/1/16: I just found a very good Baker's Math reference on the King Arthur Flour web site. Here is a link to it: Baker's percentage

Comments

1 - Formula variations can be easily expressed without having to re-calculate the entire shabang. Ex: starting with a basic baguette: "Add 20% sliced pitted olives" makes it an olive bread. "Roll in 50% shredded cheese" makes it a cheese bread. The rest of the formula would remain the same with only the total yield changing.

2 - You can scale the formula from a specific amount of any ingredient. This is especially useful when testing, but comes up often when we are slightly short of something. Ex: When testing, I like to make things easy on myself being what I call "constructively lazy." Bulk goods can be measured easily, but for things like butter or eggs, I'd rather not have little leftovers all over the place. So if a formula calls for 33% butter, and I know my butter comes in 454g bricks, I simply divide 454 by 0.33 to get 1376 (rounded) which is my flour weight and go on from there.

3 - The BP system, through convention, always uses flour as the basis. The same idea can be applied to other products that use some other major ingredient so long as it is mentionned as being the basis. This is useful for products that use no flour, or very little. For example, this recipe for creme a flan looks wierd:

AP Flour

100.00%

35% Cream

1000.00%

Whole Egg

440.00%

Sugar

200.00%

1740.00%

If we re-state it using 35% cream as the basis, it looks better.

35% Cream

100.00%

AP Flour

10.00%

Whole Egg

44.00%

Sugar

20.00%

174.00%

Both ways work perfectly well, but, I don't know, the second just seems easier to me. Of course, for something that uses no flour at all, choosing another basis is your only option. Ex Cream Cheese filling:

Not to be disagreable (moi?), but we usually refrain from calculating baker's percentages on the final dough - for the very reason you stated - if there is a pre ferment involved, it isn't useful in understanding the composition of the product.

Why you leave out the altus is also a mystery to me.

And then there is the baker's math convention of recording the percentage of pre fermented flour - which is a critical factor.

Time to log on to the BBGA website and refresh your understanding.

Baker's math is a great tool. I have fooled around with variations, but in the final analysis, there are very good reasons for the standard. You are respected here on these pages and promoting it would be a great thing.

We often leave out the altus simply because we don't have any ready, or we don't have leftover rye bread to soak, or we don't have the time, etc

IMHO: Makes a difference, but not a huge one.

Another point: we routinely calculate BP on final dough, not so much to judge composition, but more because it aids in mise en place and stock forecasting. Some guys use it, others don't. Not a big deal either way.

your comment - but why leave it out of the formula if you are doing a tutorial was the intent of my ponderings. There is a way to include it.

No biggie on the bakers percentage on the final dough - you are right. I am kind of interested as to why the percentages help with mise en place and stock forecasting (because I'm all for making my life easier - trust me) and my tiny mind can't quite come up with a reason why they would and would welcome your thoughts.

But what about stating the percentage of pre fermented flour in the formula? To me that is a biggie because it aids in understanding the nature of the formula and provides a good startng point if you are then modifying the formula - as in "I like this formula, but I wonder what a firm pre ferment would do?" More easily calculated if you do the work with the percentage of pre fermented flour.

The BBGA standard on bakers math are pretty recent and have not been universally adopted, but I'm a big supporter because once you get your mind around them, they actually make life easier.

Why, anybody can have a brain. That's a very mediocre commodity. Every pusillanimous creature that crawls on the Earth or slinks through slimy seas has a brain. Back where I come from, we have universities, seats of great learning, where men go to become great thinkers. And when they come out, they think deep thoughts and with no more brains than you have. But they have one thing you haven't got: a diploma.

Re: Mise en place: Not quite sure since I never use it for that purpose. I do however have a couple of guys who insist on doing so, and said it helped with their mise en place. For all I know it may be just a habit, or the way they were originally taught. I guess I can ask them on Tuesday, although I don't usually like to stick my nose in another man's methods, especially when they seem to work for him.

Re: Stock forcasting: In the early days, I would often run out of stuff. I eventually set up my formulae with every ingredient listed so that I would know exactly what I needed for a given degree of production. Every formulae to be used in a week would then be consolidated into one beast of a formula , in kg not %, based on the expected production. I would then place my orders accordingly. I found that by applying BP to the final dough, with the preferment itemized, it was easier on me to write the spreadsheet. Now that I think about it, it probably would have been just as easy to use normal percentages, but I didn't think of it then.

Actually, the spreadsheets, as I remember them, were quite similar to the BBGA ones except that everything was put together in one itemized list. Please remember that the spreadsheets were not used for production, but only to determine how much of which ingredient I needed.

Nowadays, the accounting system handles that particular headache way better.

you don't need to stick your nose in if you don't want to... (But I'dd love to know - because I can see why the weights help, but not the percentages)

The "hobby" that supports my baking is implementing large scale Supply Chain Planning systems and that includes inventory management, etc. That's kind of where my mind went - just as easy to use normal percentages.

Yep - there are pretty nice systems that take care of the stocking issues... (but you wouldn't use the one I implement unless you had a very, very large bakery...)

Just to be clear - it's percentage of pre fermented flour - not dough. You've paid for the membership give the site a look :>)

I'll hold my judgement on the final dough percents until PastryPaul can enlarge my tiny mind with details on how it is useful. If it is, it's worth calculating - if not - as we've all said - it can be confusing. When you write up your formulas for Breadlines though, they will ask you to leave it out.

How to handle altus - well, if you are just crumbling up old bread and adding it to the final mix, it would be included just as any other ingredient (as would the carroway seed or any other additional ingredient). If you are soaking the stuff in water you would add two lines and one column to your formula, The two lines would be "rye bread" and "soaker water". The column would be "Soaker" and would contain the amounts and the percents. The rye bread would be 100% in the soaker column (and the theory on this - if you are extending this to all soakers would be to use the sum of the things you are soaking - similar to the totals of flour) and the water percent calculated against this. In the overall formula, you would calculate percents of each of these ingredients against the total flour. Of course, your soaker would be "hydration neutral" which is a great theoretical concept - but as many of us have found out is harder to do in practice.

I have become a total formula dweeb... I can actually do this from memory...

My brain no like, probably because I've moved my entire thought process "whole hog" to the BBGA format, which I understand at a glance.

For me, a formula must be reductive. It reduces the complexity of relationships to component parts. All of those parts must be obvious (where's the altus?), the relationships between them must be obvious, and the math must check.

When I look at formulas like the one you posted above (and you're always generous with them, thank you!), my brain just wants to reject them outright.

Let me unblock the adenosine receptors in my brain with a big cup of coffee and see if I can reformat as BBGA. Perhaps the contrast will show the advantages.

I thought to myself, "It's bread crumbs, so how much do bread crumbs weigh?" When I add altus, it's just the leftover bread crumbs from an old rye loaf. I don't soak it, so don't think of it as a soaker). Minioven's going to reproach me for this.

(Note that the other ingredients are based off of total dough weight, not total flour weight). I don't know if that's the formal way to represent them, but that as best as I can determine based on the details published by the BBGA. Anyone know if I'm doing that right? Wrong? If wrong, help please.)

I have a good enough understanding about the Bakers % and your table makes perfect sense, however, is it not necessary to count the flour and water used in the 10 grams of see culture? I guess if it is such a small amount it really wouldn't matter right?

I am a bit confused by the 'conversion factor' above. If we are calculating off of the flour being 100% and we know the % of each item in the formula why not simply multiply the % of each ingredient needed against the total amount of flour in the recipe? Isn't that a more direct way to work out amounts needed???

Eg I have 1000g of total flour in a recipe and I know the water amount will be 65%....to get the quantity of water needed wouldn't it be simpler to multiply 1000 x 65% and thus end up with 650g of water? And then continue down the line with all the rest of the ingredients?

If I try using this with your formula above my answers aren't the same as the ones you arrived at by using the conversion factor so I am not sure which method is 'correct' here.....

As PastryPaul noted, the two methods will yield the same results. The benefit of using the conversion factor comes when you want to scale the size loaves. For example, David's formula makes a batch of 1200 gm. After baking loss, your final loaf might be around 1000 gm. Say you wanted to make two 1 lb loaves (total about 900 gm). You could multiply the formula by 0.9, or instead you could modify the factor. In other words, multiplying the ingredients by the BP is a top-down approach, while using the conversion factor is a bottom-up method where you define what you want for a final product and determine the ingredients to get that result. Granted, this is much more important to the professional baker than to the home cook, but it's another useful tool to have at your disposal.

You can calculate ingredient amounts either way. Your suggestion works best if you are starting with a known quantity of one ingredient. The conversion factor calculation works best if you know the total weight of dough you want to mix. It seems to me the latter situation is more common.

Thanks All for clarification here. My head spinning is slowing and the room is coming into focus once more.

Once I learned how to use WY as leavening I began to prefer using it rather than IY in most of my breads which meant I had to figure out how to convert IY recipes to WY ones. The easiest way I could figure out how to do that was by finding out the total amount of flour in the recipe I wanted to convert. Once I had found out the flour amount all other %'s were easy to figure based on simple division. It also provided me with a quick and easy way to determine the amount of flour needed in my leaven by simple multiplication......I could then expand even further by simply plugging any amount of dough I want to make by using all of my original %s and a bit more division.

When reading about a 'conversion factor' I began to wonder if I had missed an important step somewhere. I now understand that I haven't but I still don't understand why someone would use a 'cf' as it appears as though it requires adding an extra step in the process. I can still use my original % figures and get any amount of dough I want by simple division too...

In my current way of doing this I use the %'s as my 'base' and can do pretty much anything I want to with them. If I am understanding the 'cf' method it seems like I would be using the current formula's weights rather than the %'s as my 'base' and would always be relying on the original weights listed in a specific formula. With my method I can simply look at a list of ingredients and their %'s without any weights at all and I have enough information to build any size of loaf I want to.

I guess I am not clear on why you have said the 'cf' works best 'if you know the total weight of dough you want to mix' when it appears as though I can use my method just as easily or am I not seeing something really obvious here???

Sorry for the questions.....maybe I am simply over-thinking things here....

Almost but now my head is really spinning and I am thinking I have this all totally wrong....

First is the total % you are using as your original dividing #. Where did you get that figure? When I add up all the % you have listed I only come up with 173% so anything I come up with trying to see if I can get the hang of this is way off of your figures.

Maybe it is best to show you what I am currently doing so you can 'see' it and let me know where I have gone off track.

If I were to see a formula posted or written somewhere such as this:

Flour: 100%

Water: 65%

Salt: 2%

Total % : 167%

( I am keeping this really simple because that is all that my brain can handle right now :-)

Now I decide I want to make enough dough to make 2 loaves of bread each weighing 700g so I will need 1400g dough.

Next step: 1400/167% = 838g which, I have always assumed, is the total amount of flour I would need in the recipe.

So now I have my 100% flour amount and I can simply multiply the rest of the % figures to give me the rest of the ingredients thus:

Flour: 838g

Water: 838 x 65% = 545g

Salt: 838 x 2% = 17g

I then add all of the total weights up and I arrive at my desired 1400g

If I want to decrease the final amount of dough to only 500g I then would repeat the above process with the adjusted total flour amount which I obtain by division: 500/167% = 299g and then I am off and multiplying all over again.

When converting to wy from an iy yeast recipe I simply multiply the total flour amount by the percent of pre-fermented flour I want to use and I then know how much of the total flour to deduct for my leaven builds and the remaining flour goes into the final mix.

Once the conversion factor is known, everything else in the recipe is easy to derive:

Recipe with (75% rye, 25% white flour, 70% water, 1% yeast, 2% salt):

Monday - Friday (5 kilos)

What is conversion factor? ----> 5 kg/(173/100) = 2.89)

75% rye * 2.89 = 2.168 kg

25% white flour * 0.723 = kg

70% water * 2.89 = 2.023 kg

1% yeast * 2.89 = 0.029 kg

2% salt * 2.89 = 0.0578 kg

Saturday, Sunday (10 kilos)

What is conversion factor? ----> 10 kg/(173/100) = 5.78))

75% rye * 5.78 = 4.335 kg

25% white flour * 5.78 = 1.445 kg

70% water * 5.78 = 4.046 kg

1% yeast * 5.78 = 0.058 kg

2% salt * 5.78 = 0.116 kg

HOLIDAY RUSH (37.6 kilos)

What is conversion factor? ----> 37.6 kg/(173/100) = 21.73))

75% rye * 21.73 = 16.298 kg

25% white flour * 21.73 = 5.433 kg

70% water * 21.73 = 15.211 kg

1% yeast * 21.73 = 0.217 kg

2% salt * 21.73 = 0.435 kg

You didn't go wrong.

You find total flour weight (by deciding how much dough you want and then divide by total of percentages to get total flour weight) the same way I do and use it as your 'conversion factor' to derive all the other quantities.

Your method is identical, you just don't call it a 'conversion factor'.

The head has finally stopped spinning and I can now go on my merry way without having to re-do all of the math for all of the loaves I have baked in the past year using my little method....what a load off of my shoulders :-)

I don't think you did go wrong anywhere. I don't use the conversion factor method - I just do as you do. Different styles for different people, I guess.

I was challenged in a class to convert a formula to make a given weight of bread and promised a raise if I got it exact and to be fired if I didn't. I got the answer way before the rest of the class becuase I used the same method as you. And I wasn't even using a calculator. Never did get that raise, though...

Anyway, as another interesting tale of baker's math - for the scoring at the Coupe du Monde, one of the factors is the amount of dough waste. The bakers must make a specified number of loaves at a specified weight - so they'd better get the math right because if they mix too little they are completely out of luck, but if they mix too much - points will be taken...

Thanks for letting me know that I haven't gone totally astray with my little math gymnastics. I was feeling so proud of myself for finally being able to use the math I learned in school for something other than balancing a check book and paying bills that when the thought hit that I might be doing it all wrong by forgetting a key element I suddenly felt like I was sitting for a final exam and realizing I had studied all the wrong material. Interesting how those feelings come flooding back.

With your little tale above I am thinking that I will withdraw my application to compete in the next Coupe du Monde :-) Amazing what they find to judge the teams on. Do they get points for keeping their work space and themselves clean? Maybe I could tag along as a kitchen wench :-)

Anyway, I am relieved my figures are all safe in their little binders. I will now be able to sleep soundly tonight.

Janet

P.S. I am impressed that you could do all the math calculations in your head. That I can't do without my trusty kitchen calculator unless the amount of flour is divisible by 10 or 100 or 1000....

on an incredible array of things - including the cleanliness of the workspace during and after the bakes. Four years ago when I spent more time in the stands and less on bakery tours, I heard discussion that someone had stuffed a broken suitcase with various baking detritus and left in in Team USA's workspace. Then pointed it out to a judge (oh, the little scandals...)

And they are required to clean up after themselves. So after a full day of breakneck baking, they get to sweep up their laboratoires. Geez.

But this year - finishing on time - was a big, big deal. Brave little Team Senegal - who, in my book was a serious winner just to get to the Coupe - didn't finish even after the grace period - and a lot of the European teams didn't finish on time. There is a reason that we celebrate those bakers who make it there - they are seriously skilled.

I was probably the last of the people who finished engineering school using a slide rule - some skills remain...

So scullery maid might be a possibility after all....my horizons expand :-)

Amazing indeed what is involved....little does the public now!

Yeah for slide rules. I am sure you have a much clearer understanding of the relationship between figures then those who come up with answers by using calculators....seems like many now simply do not care for the 'ground' from which most things spring. The end 'product' being the goal by any means possible. I say to this mentality - how sad because it has been my experience that it is from these very 'details' that all the possibility springs forth - all the mystery to begin with...

but that is a huge generalization as I know there are many indeed who grasp things infinitely larger than I can even imagine all with the use of calculators and other hi-tech equipment....where would our understanding of the Universe be without the use of computer operated telescopes or medical science without the aid of the atomic microscopes ....the list goes on

and I am rambling and way off topic.

The End!

but....

I love the math involved in baking, as you have stated, because the numbers do tell me about the doughs I am working with. It grounds me and expresses things clearly in a way that words can be very misleading I never would have know about it had it not been for this site. I did look up the info. from the site you mentioned and found it very interesting that the math I have been doing since learning about it has led me to the same end that their charts display....was sort of a natural evolution once I leared the simplicity of how to use the %'s. If my memory is correct I do think it was Ananda who first pointed out the % 'trick' and it instantly opened up a whole new world of possibilities to me. You can probably understand a bit of the angst I felt when I though that maybe my method had led me astray somehow.....nice to know it has not....huge relief :-) Also nice to know that I stumbled upon something that led to what the baking world has decided upon as a 'standard'.....the beauty of it is it's absolute simplicity - in my opinion....

I think in terms of the final product - how many loaves of what weight. So the approach in the tutorial is the one I prefer, generally. Unless you had some extra something you wanted to use up, I'm not clear why one would want to base a formula on the amount of a single ingredient.

Either way works (start with dough weight or flour weight), however, my reasoning is that: flour is the main "expanding" component in breads. If two breads have the same dough weights, but one has much more add-in ingredients such as nuts, dried fruit, etc, I doubt they will expand to the same volume. In the end, either way would probably work, just a matter of habit.

Okay. We have established that there is more than one way to skin a cat. In actuality, I use both Janet's approach and the one I presented. I also use an even simpler approach on occasion. When I have a recipe and want to make some fraction of the total dough, say half a recipe, I just divide each ingredient by the appropriate number or multiply by the decimal equivalent. This works too.

My question is, which method is best to teach to a person who has never used baker's math before? For the sake of argument, I would say that the method I presented is the best way to get an understanding of the principles underlying baker's math, even if it's not the simplest. When I first started using baker's math, I just took the formulas from a book (I can't recall which one right now.) and ran the numbers. It was like learning a song in a language you don't speak. The "aha! moment" came when the conversion factor was explained as representing the value of a single "unit" of the total dough content. Then, since the total flour is always 100 "units," etc., the rest just made complete sense to me.

I realize in my coffee-fueled BBGA pontification, I failed to say thank you for your tutorial.

Thank you!

I internalized baker's math a few months ago (having gone years with just following recipes). Now that I know it, I feel like I can call myself a baker, not just a person who can bake. It's a huge difference and baker's math is the genesis of the change.

I do wonder if we're getting ahead of amateur baking, which is TFL's mission. When Floyd banishes us to the Advanced forums to commiserate alone, we'll know the answer.

And thank you! They say that one really good way to learn is to have to teach. I certainly learned a few things from this exercise.

Re. TFL's mission: My sense is that it has to be accessible to beginning or even aspiring beginning bakers. But baking, like most any worthwhile endeavor, is a developmental process. One of its attractions for many of us is the opportunity to face new challenges and acquire new knowledge and skills.

This forum has accumulated a wealth of information on techniques. The best discussions, in my view, have included both practical information for the home baker and technical discussions which are probably of interest to fewer members. I'm thinking of the various discussions of home oven steaming, or those on home grain milling. A TFL member can skip the more advanced input at will, but it's there when he/she is ready to take the next step in developing expertise.

One of the most pleasurable phenomena for me has been to see a member come in asking for the most basic information and a few months later showing us truly magnificent breads they have baked. I could name names, but I won't. I will say I count myself among them, and some I've helped have surpassed my own skills. So I'd say, "It's working." Ain't it great?

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